1. Adaptive algorithm for determining limits of T wave in ECG waveform By Ashwin Panchbhai Sudheer Poojary

2. Objective Study/Implement an adaptive algorithm to determine limits of P and T wave. The following criteria dictate the use of an adaptive algorithm Oscillations in the baseline of the typical ECG. Adoption of different criteria among cardiologists.

3. Approach: In the filtered ECG, the end of T wave is near to the minimum In the filtered ECG, the end of T wave is near to the minimum Using Adaptive filtering, this minimum is shifted to the location of end of the T wave. Using Adaptive filtering, this minimum is shifted to the location of end of the T wave.

4. The transfer function for the filter is given by The transfer function for the filter is given by E(z)/P(z) = (1 + z -1 )/(1 – (1 – ).z -1 ) E(z)/P(z) = (1 + z -1 )/(1 – (1 – ).z -1 ) where is the adaptation constant. where is the adaptation constant. The initial value of  is determined by the cardiologist’s criterion. The initial value of  is determined by the cardiologist’s criterion. Using this initial value, Using this initial value, filtering is carried out which gives new value of . filtering is carried out which gives new value of .

5. Contd… After second filtering, the points where the derivative of the filtered signal is zero gives the desired limits for T wave. After second filtering, the points where the derivative of the filtered signal is zero gives the desired limits for T wave. Assumptions made : Assumptions made : The sampling rate is large enough so that is sufficiently small.The sampling rate is large enough so that is sufficiently small. In the segments from peak of T wave to the limits of T wave, the derivatives of close samples are similar.In the segments from peak of T wave to the limits of T wave, the derivatives of close samples are similar.

6. Mathematical development e(n) – .e(n-1) = ecg(n)–ecg(n-1) e(n) – .e(n-1) = ecg(n)–ecg(n-1) e’(n) = (-1).e(n-1) + d(n) e’(n) = (-1).e(n-1) + d(n) d(n) = derivative of the ecg signal d(n) = derivative of the ecg signal e’(n) is equated to 0 to give e’(n) is equated to 0 to give minimum which gives minimum which gives d(n)/e(n-1) d(n)/e(n-1) From the recursive equation for d(n) we get the time constant for the exponential averaging as From the recursive equation for d(n) we get the time constant for the exponential averaging as  = 1 /   = 1 / 

7. contd … contd … In the segments from the peak of T to the limits of the wave, the derivative of ecg signal (close symbols) are similar. In the segments from the peak of T to the limits of the wave, the derivative of ecg signal (close symbols) are similar. d(n) ≈ d(n-r-1) 0≤r≤N d(n) ≈ d(n-r-1) 0≤r≤N Hence we can have an approximation of  by making  = N Hence we can have an approximation of  by making  = N Hence first approximation is- ≈ 1/N Hence first approximation is- ≈ 1/N The cardiologist marks the limit of T wave which is used in determining value of for second filtering. The cardiologist marks the limit of T wave which is used in determining value of for second filtering.

8. Implementation ECG signals, of length 3000, sampled at 350 Hz were obtained from MIT-BIH database. ECG signals, of length 3000, sampled at 350 Hz were obtained from MIT-BIH database. The input signal was low pass filtered with 45 Hz cut-off frequency. The input signal was low pass filtered with 45 Hz cut-off frequency. The signal was interpolated to increase the number of samples in a given segment. The signal was interpolated to increase the number of samples in a given segment. The end point of the first T-segment is obtained from cardiologist's criterion. The end point of the first T-segment is obtained from cardiologist's criterion. Filtering of the signal was performed as mentioned before and the end points of the T-wave were obtained. Filtering of the signal was performed as mentioned before and the end points of the T-wave were obtained.

9. Results Fig. shows the plot of the original signal and the filtered output. Fig. shows the plot of the original signal and the filtered output. The local minimum after the T wave of the filtered signal can be seen near the end of the T- wave in the original signal. The local minimum after the T wave of the filtered signal can be seen near the end of the T- wave in the original signal.

10. Results cont.. Fig shows the limits of the T-wave for the original signal Fig shows the limits of the T-wave for the original signal

11. Limitations The algorithm does not give correct results if the ECG signal is highly abnormal. The algorithm does not give correct results if the ECG signal is highly abnormal.

12. References Application of Adaptive Signal Processing for Determining the Limits of P and T Waves in an ECG Emilio Soria-Olivas, Marcelino Martinez-Sober,Javier Calpe- Maravilla,Juan Francisco Guerrero-Martınez, Javier Chorro-Gasco, and Jose Espı-Lopez.